Time-optimal Motion Research Articles

Identification of physically consistent dynamics parameter of the ABB IRB 360-6/1600 delta robot and its use for time-optimal motion planning under consideration of constraint forces

Model-based control schemes, forward dynamics simulations, constraint force computation and time-optimal motion planning have one major thing in common, they all depend on the dynamics parameters of the system. Physical consistency of the dynamics parameters ensures a positive definite mass matrix and correct constraint forces. The most common inverse dynamics identification method – the base-parameters – lack physical consistency. This paper proposes an identification method to identify physically consistent dynamics parameters for Delta-like robots while further showing the effects of friction in passive joints. A tailored model to compute the crucial constraint forces appearing in the mechanism based on the identified dynamics parameters is derived. This model is used to additionally consider constraint forces besides actuation torques for time-optimal motion planning of a typical pick and place task. This is done without any prior CAD data of the robot from the manufacturer.

Time-optimal surveillance between two differential drive robots with a limited field of view

Keeping an intelligent agent under surveillance with an autonomous robot as it travels in the environment is one of the essential tasks in robotics. This work addresses a pursuit-evasion surveillance problem between two Differential Drive Robots moving on a plane without obstacles. One of them, the pursuer, is equipped with a limited field-of-view sensor and aims to maintain the other robot (evader) inside its detection region for as much time as possible. On the contrary, the evader wants to escape as soon as possible. Unlike prior studies that address the same problem, based on heuristic approaches, we frame it as a zero-sum differential game, and we use differential game theory to find a solution with theoretical guarantees. In particular, we compute the players' time-optimal motion strategies to achieve their goals near the end of the game and provide analytical expressions describing them. These strategies are in Nash equilibrium, meaning that any unilateral deviation by a player from these strategies does not provide such player benefit toward its goal. Our analysis exhibits the existence of a Transition Surface in which the evader switches its controls. We also determine the game's winner based on the players' initial configurations and velocities.

Time-Optimal Motions of a Mechanical System with Viscous Friction

Optimal control is a critical tool for mechanical robotic systems, facilitating the precise manipulation of dynamic processes. These processes are described through differential equations governed by a control function, addressing a time-optimal problem with bilinear characteristics. Our study utilizes the classical approach complemented by Pontryagin’s Maximum Principle (PMP) to explore this inverse optimal problem. The objective is to develop an exact piecewise control function that effectively manages trajectory control while considering the effects of viscous friction. Our simulations demonstrate that the proposed control law markedly diminishes oscillations induced by boundary conditions. This research not only aims to delineate the reachability set but also strives to determine the minimal time required for the process. The findings include an exact analytical solution for the stated control problem.

Surveillance evasion between two identical differential drive robots

This paper addresses the problem of keeping a Differential Drive Robot (evader) inside the detection region of another Differential Drive Robot (pursuer) equipped with a bounded range sensor. The sensor is modeled as a circle centered at the pursuer’s location. The pursuer’s goal is to maintain surveillance of the evader for as long as possible. The evader has the opposite objective and wants to escape from the pursuer’s sensor as soon as possible. The players are modeled with two discs with the same radius and move in a plane without obstacles with the same maximum speed. In this work, we find the time-optimal motion strategies of the players to achieve their goals. We also analyze the problem of deciding the winner of the game, that is, determining under which conditions the evader can escape from the detection region.

Path-Constrained Time-Optimal Motion Planning for Robot Manipulators With Third-Order Constraints

Planning time-optimal motions of robot manipulators is important for maximizing productivity in industry and has attracted much attention in academia. Time-optimal time scaling (TOTS) of specified paths subject to second-order constraints is a well-studied problem in robotics. However, there is still a lack of effective approaches for computing TOTS with higher order constraints. This article proposes a novel method for TOTS subject to third-order constraints. The proposed method formulates the third-order TOTS as a four-stage optimization involving only linear programming by exploiting the special structure of the problem. The proposed method first performs a backward pass and a forward pass to generate the second-order optimal velocity profile. Then, the points violating the third-order constraints are identified, and the constraint violations are eliminated through numerical integration around the violating points. A bisection search algorithm is proposed to quickly determine the switching points at which the elimination process begins. The proposed method is verified through numerical examples and experimental tests. The results indicate that the proposed method outperforms the state-of-the-art approaches in terms of solution quality and computation time.

Real-time motion planning for an autonomous mobile robot with wheel-ground adhesion constraint

The paper proposes a new real-time motion planning technique for an autonomous mobile robot that is able to find a collision-free path and a corresponding time-optimal trajectory while taking into account limits on the actuator capacities and constraints from the wheel-ground adhesion. The proposed technique includes two sub-modules. The first one, an optimal path planner, is based on the discretization of the robot workspace and dynamic programming principle. It allows finding the shortest path in the robot environment to avoid obstacles and reach the robot target. The second one, an optimal trajectory generator, operates with the discretized robot state-space and also employs dynamic programming techniques. It produces a time-optimal motion along the obtained path, which may include numerous regular and singular trajectory sections caused by the simultaneous application of actuator and wheel-ground adhesion constraints. To adapt this technique to real-time implementation, a moving window strategy is presented that allows regularly updating the robot motion profile in a dynamic environment. The advantages of the developed technique and its suitability for real-time control are illustrated by experimental studies implemented on a car-like mobile robot.

Point to point time optimal handling of unmounted rigid objects and liquid-filled containers

Time optimal handling of parts loosely placed at the end-effector (EE) of a robot, known as waiter motion problem, has high practical relevance, which becomes more challenging if the object is a liquid-filled container. The waiter motion problem was often restricted to a time-optimal path following problem, which limits the flexibility and task efficiency. To overcome this restriction, in this paper, the general point to point (PtP) time-optimal motion planning problem is formulated and solved with a multiple shooting method. The formulation includes all relevant dynamic effects (joint friction, contact, motor limits, etc.) assuming rigid behavior of the robot as well as of the object placed at the EE. The trajectory is C2-continuous, avoiding bang–bang behavior of motor torques. The CasADi framework and the Ipopt solver are used for numerical computations. The reported experimental results confirm applicability of the trajectory to real robotic setup in case of rigid objects. Further, handling of containers filled with liquid is addressed. Experiments are compared with numerical results obtained with SPH particle simulation. Experiment and simulation indicate that sloshing effects must be taken into account in the control formulation.

Generation and experimental verification of time and energy optimal coverage motion for industrial machines using a modified S-curve trajectory

Generation and experimental verification of time and energy optimal coverage motion for industrial machines using a modified S-curve trajectory

Active learning of time-optimal motion for an industrial manipulator with variable payload

Generating optimal motion for robotic systems remains an active field of research, despite its relatively long history. In addition to being optimal with respect to a defined cost, such a motion must respect the electro-mechanical limitations of the system to be of use in real-world applications. Furthermore, in an industrial application where offline planning is not possible due to a priori unknown targets and payloads, the available time budget for computations is often highly limited, making many optimal motion planning approaches unsuitable. This work introduces a supervised learning-based motion planner for industrial manipulators that closely retains the superior performance of an optimal motion planner while requiring a fraction of the computations at runtime. The proposed motion planner implicitly considers the dynamics of the robot and therefore satisfies not only kinematic limits but also those of the actuators. The proposed method is compared to state-of-the-art approaches and demonstrated on a real robot.

MPC-based Motion Planning for Autonomous Truck-Trailer Maneuvering

Time-optimal motion planning of autonomous vehicles in complex environments is a highly researched topic. This paper describes a novel approach to optimize and execute locally feasible trajectories for the maneuvering of a truck-trailer Autonomous Mobile Robot (AMR), by dividing the environment in a sequence or route of freely accessible overlapping corridors. Multi-stage optimal control generates local trajectories through advancing subsets of this route. To cope with the advancing subsets and changing environments, the optimal control problem is solved online with a receding horizon in a Model Predictive Control (MPC) fashion with an improved update strategy. This strategy seamlessly integrates the computationally expensive MPC updates with a low-cost feedback controller for trajectory tracking, for disturbance rejection, and for stabilization of the unstable kinematics of the reversing truck-trailer AMR. This methodology is implemented in a flexible software framework for an effortless transition from offline simulations to deployment of experiments. An experimental setup showcasing the truck-trailer AMR performing two reverse parking maneuvers validates the presented method.

Time-optimal general asymmetric S-curve profile with low residual vibration

This paper presents a novel optimization process for the proposed general asymmetric S-curve (AS-curve) profile to achieve fast movement and low residual vibration. The general AS-curve profile, which is the superset of traditional symmetric S-curve and prior asymmetric S-curve profiles, enables independent manipulation of accelerations and jerks at the starting and arrival phases. To minimize the positioning time (traveling time plus settling time) while reducing residual vibration, we formulate the optimization of the general AS-curve profile by allocating the time intervals under the physical limits and the residual vibration constraints. To this end, the complete solutions to the general AS-curve profile are provided to construct physical limits. By executing the point-to-point motion profiles with different motion parameters and measuring the residual vibration signals, we obtain a surrogate numerical model using the multi-task Gaussian process regression to construct the residual vibration response, and then utilize this model to predict the settling time and maximum residual vibration amplitude. Finally, the time-optimal motion profiles are validated by the 7-DOF Sawyer robot showing that the proposed motion profile optimization method is capable of reducing the residual vibration significantly compared with the traditional symmetric S-curve.

Safety-Aware Time-Optimal Motion Planning With Uncertain Human State Estimation

Human awareness in robot motion planning is crucial for seamless interaction with humans. Many existing techniques slow down, stop, or change the robot's trajectory locally to avoid collisions with humans. Although using the information on the human's state in the path planning phase could reduce future interference with the human's movements and make safety stops less frequent, such an approach is less widespread. This paper proposes a novel approach to embedding a human model in the robot's path planner. The method explicitly addresses the problem of minimizing the path execution time, including slowdowns and stops owed to the proximity of humans. For this purpose, it converts safety speed limits into configuration-space cost functions that drive the path's optimization. The costmap can be updated based on the observed or predicted state of the human. The method can handle deterministic and probabilistic representations of the human state and is independent of the prediction algorithm. Numerical and experimental results on an industrial collaborative cell demonstrate that the proposed approach consistently reduces the robot's execution time and avoids unnecessary safety speed reductions.

Time-optimal robotic manipulation on a predefined path of loosely placed objects: Modeling and experiment

A consistent method is presented for solving the so-called general waiter problem, which is to move a tray (mounted at the end-effector of a robot) with a number of loosely placed objects (e.g. cups) as fast as possible such that the objects do not slide at any time. The geometric path of the tray motion is prescribed while the attitude of the tray must vary in order to avoid sliding or tip-over of the objects. The time optimal robot trajectory is determined with a multiple shooting method. For the considered wrist-partitioned robot, the motion is described by the path parameter and the three joint coordinates of the wrist. This 4-parametric description is beneficial for solving the optimal control problem with improved convergence. The optimization takes into account the technical limitations of the robot as well as the limiting friction between objects and tray. Experimental results for a time-optimal motion of a Stäubli RX130L manipulating a tray with 4 cups are presented. A crucial aspect is the use of a model-based control strategy along with the identification of dynamic parameters. Moreover, the basis for any optimization and real-time control is a reliable dynamic model of the robot. Therefore a parameter identification is performed using optimized persistent excitation trajectories.

A predictive neural hierarchical framework for on-line time-optimal motion planning and control of black-box vehicle models

This paper addresses the on-line minimum-time motion planning and control of a black-box racing vehicle model. We present a hierarchical control framework, composed of a high-level non-linear model predictive controller (NMPC) based on an advanced kineto-dynamical vehicle model, a low-level neural network to compute the inverse steering dynamics and a longitudinal controller for the low-level tracking of speed profiles. An off-line identification procedure, consisting of simulated manoeuvres, is defined to learn the high-level and low-level models. A closed-loop simulation is setup to control the black-box vehicle near the limits of handling along a racetrack. Simulation results are compared with the off-line solution of a minimum-time-optimal control problem.

On some regularization of the control problem for a tracked mobile robot in a steady flow field under state constraints

In this article, we consider the time-optimal motion control of a tracked mobile robot in the presence of state constraints. The complexity of the problem statement is due to a steady vector flow field in which the motion is takes place. The difficulty of the considered model is also compounded with the non-regularity of the dynamics with respect to the state constraints. A method for regularisation is proposed. Such a method involves a certain construction of a regular (in the needed sense) ε-perturbation of the original problem.

Capturing a Dubins Car With a Differential Drive Robot

In this paper, we study the problem of capturing a Dubins Car with a Differential Drive Robot in minimum time. The two vehicles are represented like unitary discs moving in the plane without obstacles. Both agents have the same maximum speed and a bounded turning ratio. We frame the problem as a pursuit-evasion game. The Differential Drive Robot plays as a pursuer and aims to capture the Dubins Car as soon as possible. The Dubins Car, on the contrary, takes the evader’s role and tries to avoid capture. Using differential game theory, we compute the players’ time-optimal motion strategies to accomplish their tasks and provide analytical expressions describing them. In particular, we reveal four singular surfaces in this game. Two evader’s dispersal surfaces (EDS) where the evader can choose between two controls and the pursuer must react accordingly, leading to trajectories with the same cost. One pursuer’s dispersal surface (PDS) where the evader must select its control based on the pursuer’s choice. And a transition surface (TS), where the DDR switches its controls. Some examples of the players’ time-optimal motion strategies are shown in numerical simulations.

Time-optimal trajectory planning of manipulator with simultaneously searching the optimal path

Time-optimal trajectory planning can improve the efficiency of the manipulator, which has a paramount research significance. Nonetheless, almost all the current algorithms have the problem of path limitation — the algorithm constantly searches for the optimal motion time of the manipulator on a specific motion path. To solve this problem, we design a time-optimal trajectory planning method for the manipulator by searching the optimal path simultaneously. We propose using a cubic uniform B-spline interpolation algorithm to derive the motion curve expression of the manipulator joint with unknown path points. Then we use a genetic algorithm to optimize the path point and the motion time of the manipulator at the same time to get the time-optimal motion path of the manipulator. Moreover, we prove that the algorithm proposed in this paper is comparable with similar algorithms with known paths through experiments.

Optimal Reference Trajectory for a Type Xn-1Rp Underactuated Manipulator

The aim of the present research is to find an optimal reference trajectory for an underactuated manipulator of type Xn-1Rp, where X is any type of joints and R is the last rotary joint, for n≥3. It is worth noting that in the case of absence of control of fully actuated manipulator, some second-order nonholonomic constraints may appear; these are known as acceleration constraints. The second-order nonholonomic constraint is a non-integrable differential equation. For this purpose, it was decided to combine two methods. The first one provides the open-loop control of the manipulator whatever the motion time is; in practice, the motion time should be minimal under the given geometric, technological, and dynamic constraints. To address this issue, a second method, based on the offline optimization approach, was used to achieve the time-optimal motion. It was revealed that the above combination gives an optimal control trajectory for an underactuated manipulator in which a reference trajectory can be utilized.

Single landmark feedback-based time optimal navigation for a differential drive robot

In this paper, we propose a feedback-based control approach to execute the time optimal motion trajectories for a differential drive robot. These trajectories are composed of straight lines and rotations in place. We show that the evolution of the position of a single landmark over time, in a local reference frame, makes it possible to track a prescribed time-optimal robot’s trajectory, based on feedback of the landmark’s position. We also show that the closed-loop system is an exponentially stable one with a nonvanishing perturbation, and that globally uniformly ultimately boundedness of the tracking errors can be achieved. The two main results of this work are: 1) Our approach leverages visual servo control type of methods with tools from optimal control for executing time-optimal trajectories in the state space based on feedback information. 2) The approach is able to work with the minimum number of landmarks–only one–this represents a necessary and sufficientcondition for landmark-based navigation. Experiments in a physical robot, a nonholonomic differential drive system equipped with an omnidirectional laser sensor, are shown, which validate the proposed theoretical modelling.

A game of surveillance between an omnidirectional agent and a differential drive robot

ABSTRACT This paper addresses a surveillance problem between a Differential Drive Robot (DDR) and an Omnidirectional Agent (OA) in a Euclidean plane without obstacles. The agent is initially located inside the robot's detection region, and it wants to escape from it as soon as possible. The DDR, on the other hand, wants to delay the escape as much as possible. The pursuer's detection region is modelled as a circle centred at the pursuer's current location. In this work, the time-optimal motion strategies for the players are presented. Also, based on the players' initial configurations, we solve the decision problem of determining the winner of the game.